In the first report over the weekend, unnamed sources told TMZ that Odom, 32, has been using "hardcore recreational drugs" for the past two years and went to rehab last August. The report claims Odom stayed clean for the duration of the basketball season but started using drugs again once his run with the Clippers ended.

Reps for Odom and the Clippers have not returned PEOPLE's multiple requests for comment. A rep for Kardashian Odom declined to comment.

A source close to the couple tells PEOPLE that Karshadian Odom has been struggling to help her husband. "It's a really hard time for Khloé," the source says. "She's kept this secret for almost two years trying to save Lamar and their marriage."

The 29-year-old "recently came clean and [her family] has been trying to help since," the source says.

Another source who has known Odom for years says the couple have clashed over his partying: "Lamar genuinely doesn't think he has a problem – it's all 'work hard then party hard' with him until it goes off the rails. They really do love each other. But she really feels that this problem is out of control, and she's hurt that he won't get help."

The couple has not been spotted together in public since June 2, and neither has commented on the status of their marriage, even following reports of infidelity allegations (which Odom has denied). On Thursday, Kardashian Odom was photographed looking unhappy and not wearing her wedding ring for a trip to the gym. On Aug. 25, she Tweeted, "Really hard to sit here and listen to people talk s--- about my family . . . I'm too protective for this s---!"

"It's absolutely heartbreaking for her," the source close to the couple says of their struggles. "This is such a heavy load."

Odom's Past Problems

This is not the first time Odom has faced drug accusations. He was suspended in 2001 when he violated NBA drug policy twice in eight months. He admitted at the time to smoking marijuana, telling reporters: "I hope everyone doesn't pass judgment on my mistake. I've made a couple and I may make a couple again, but hopefully they won't be as big as this one … This will never happen again."

His close friend and former coach Jerry Degregorio has said: "Lamar, in crisis situations, he has a tendency to want to get away and hide. He just wants to go away and hide and be by himself."

In 2012, Odom disappeared from the Dallas Mavericks for 10 days amid reports his father was ill. "It was really personal and it was something I had to tend to," he said when he returned. "There are times when we have to fix what is going on off the basketball court in order to fix what's going on on the court."

Sources say Kardashian Odom, whom he wed in 2009, has been a supportive influence. "Khloé is so insanely protective over Lamar," says another source close to the family. "Whatever they're going through in their relationship is taking a back seat to getting him better, I can tell you that."